Recent content by Bosko

I think that the answer is in the Noether's theorem. That question appears in the early stage after Einstein published the GR theory. https://en.wikipedia.org/wiki/Noether%27s_theorem

Do you think that for ##r_1 < r_s## the mathematical model does not correctly represent physical reality?

Two objects of the same mass but different radii.

Thanks. I put the topic in "Beyond the Standard Models" so as not to violate the forum rules in case someone offers non-standard thinking.

That's exactly what I thought. Edit: That is valid

In other words, for any ##r_1## and ##r_2## the solution is the same outside of ##max(r_1,r_2)##. Am I right, even if one of ##r_1## or ##r_2## is smaller than ##r_s## (Schwarzchild radius)

There is no parameter of a spherically symmetric object in the solution. For example, the radius . The solution does not depend on the size of the object. Let's find some detailed explanation of the formula and see when the radius of the object vanishes . Is this from Wikipedia good for...

It might be better to ask an equivalent question: Let two spherically symmetric objects of the same mass of radius ##r_1 \lt r_2## be given. Is the spacetime for ##r \gt r_2## the same in both cases? So a larger sphere can be replaced by a smaller ... etc ... arbitrarily smaller ... the point...

Any. Some are explicit with the point mass as the represent of the spherically symmetric object and other are using the equivalent form in one of the steps in derivation.

The first part can be derived from the second part . E.g. The array of shells with the same mass and with 1/n radius . By subtracting results of the consecutive elements of the array you can get equivalence with the point mass. Of course it is not the physical object any more but the...

I suggest you start with the formula for wavelength for an observer at infinity. $$\frac { \lambda_\infty} {\lambda_e} = \sqrt { 1- \frac {r_s} {r_e} } $$ where ##r_s## is the Schwarzschild radius

How then? Is there a point mass?

In the classical Newtonian theory of gravity, the shell theorem holds. ( https://en.wikipedia.org/wiki/Shell_theorem ) In the beginning of the derivation of the Schwarzschild solution, the spherically symmetric object is replaced by a point mass. The proof that this can be done in curved...

As an example you can consider a triangle in the plane R^2 with vertices A=(0,1) B=(1,0) C=(1,1) x<=1 y<=1 x+y>=1 ( -x-y<=-1 )

The same